Question

Find the length of the height of the cone. 13cm and d=10cm

(1 point)
cm

Answer 1

To find the height of a cone given the slant height (l) and the diameter (d), we can use the Pythagorean theorem. The formula is:

\[
l^2 = r^2 + h^2
\]

Where:
- \( l \) is the slant height of the cone (13 cm in this case),
- \( r \) is the radius of the base of the cone,
- \( h \) is the height of the cone.

First, we need to calculate the radius (\( r \)) from the diameter (\( d \)):
\[
r = \frac{d}{2} = \frac{10 \, \text{cm}}{2} = 5 \, \text{cm}
\]

Now we can substitute \( l \) and \( r \) into the Pythagorean theorem:

\[
13^2 = 5^2 + h^2
\]

Calculating the squares:
\[
169 = 25 + h^2
\]

Subtracting 25 from both sides:
\[
169 - 25 = h^2
\]
\[
144 = h^2
\]

Taking the square root of both sides:
\[
h = \sqrt{144} = 12 \, \text{cm}
\]

So, the height of the cone is **12 cm**.